*quality mindwarp.

Boosting this quality contribution up in the Hot Listing - declared quality by arvana.

Notice how easily the pieces slip into place in the first layout compared to how he has to force them into place on the second layout.

It's related to this:
http://nrich.maths.org/content/01/06/six3/triangle-illusion.gif

This is dumb. How is this "impossible," or "magic" at all? haha. Wow. Only a pathetic, feeble mind wouldn't comprehend this.

I suppose then that if the pieces were made out of precise-fit steel, they wouldn't fit in the second configuration... or would they?

Ok, I thought this was going to be an illusion... Kept waiting for the bigger piece to end up the same size as the smaller one.

Dan Secrest - The reason why there is a gap in these "triangles" is actually related to fibonacci's sequence. But I wont go there. The easy solution is simply because those are not triangles. Each has 4 sides. The red triangle has a different slope than the green. The red triangle has slope 3/8 while the green has 2/5. Therefore, in the upper "triangle" there is increasing slope along the hypoteneus and in the lower there is decreasing. The short short answer is that the areas of both triangles are EXACTLY the same, but the lower triangle has a gap to make up for the different slope it has on the hypoteneus. If anything, these resemble non-euclidean triangles because there angles add up to over 180 degrees.>> ^dannym3141:

Notice how easily the pieces slip into place in the first layout compared to how he has to force them into place on the second layout.
It's related to this:
http://nrich.maths.org/content/01/06/six3/triangle-illusion.gif

I'm totally baffled, surprise to no one.

>> ^Payback:

Ok, I thought this was going to be an illusion... Kept waiting for the bigger piece to end up the same size as the smaller one.


Exactly my point. People downvoted my comment because they're dumb, I guess.

The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.

*wtf

Adding video to channels (Wtf) - requested by maatc.

>> ^ForgedReality:

Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.

FR, if you can't see why this shouldn't be possible, you lack a basic understanding of geometry.

The area of the square is width x height. In the first configuration, the pieces cover the full area of the square. In the second configuration, they do not. The area has not changed. The pieces have not shrunk. So why is there a part of the puzzle that is empty?

If everybody else is so dumb, please enlighten us as to how this is possible.

My only guess is that the pieces are being squished into the second configuration, and the squished portions make up for the missing coverage. But that would mean this would not work with sturdier material, or in a computer model.

>> ^MaxWilder:

>> ^ForgedReality:
Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.
FR, if you can't see why this shouldn't be possible, you lack a basic understanding of geometry.
The area of the square is width x height. In the first configuration, the pieces cover the full area of the square. In the second configuration, they do not. The area has not changed. The pieces have not shrunk. So why is there a part of the puzzle that is empty?
If everybody else is so dumb, please enlighten us as to how this is possible.
My only guess is that the pieces are being squished into the second configuration, and the squished portions make up for the missing coverage. But that would mean this would not work with sturdier material, or in a computer model.


It depends how you built the rigid pieces/computer model. There ARE gaps in the first configuration, they're just small and spread. The second configuration reduces the smaller, spread gaps and converts them into one larger gap.

Check that thing i linked, you'll see that the triangle in that picture isn't a true triangle, it just looks a lot like one. It's actually got 4 sides, and you can apply something similar here.

There are plenty of such puzzles made in wood and have personally played with one of them so I'm going to guess the construction argument is moot.

>> ^MaxWilder:

>> ^ForgedReality:
Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.
FR, if you can't see why this shouldn't be possible, you lack a basic understanding of geometry.
The area of the square is width x height. In the first configuration, the pieces cover the full area of the square. In the second configuration, they do not. The area has not changed. The pieces have not shrunk. So why is there a part of the puzzle that is empty?
If everybody else is so dumb, please enlighten us as to how this is possible.
My only guess is that the pieces are being squished into the second configuration, and the squished portions make up for the missing coverage. But that would mean this would not work with sturdier material, or in a computer model.

....

Really, bro? Look at it again. Take two letter L's .. Flip one so that it is inverted, and move it so that the longer bits are touching. Now move them so that the shorter bits are resting on the longer bits of each other. Look there's a hole. Creepy huh?

What's happening is the area that the L-pieces are inside of becomes NARROWER and TALLER (since the two larger pieces are different sizes (One is wider and taller than the other, but the angle cut is the same angle, so they both fit along that edge), allowing for the L-pieces to shift into the second configuration and still fill out that space, but create a hole between them.

It's seriously not that fucking complicated. The fact that nobody here seems to understand how it works is really the only mystery here. It's quite surprising, and at the same time, it makes me worry for the future of humanity. This is no mindwarp. It's simple geometry.

I think people downvoted your comment because you were acting like a self-righteous prick.

It's also funny that your last comment (^right there) shows that you really don't understand how this works, either; you're just unaware of the reasons why this shouldn't work.

I didn't realize what was going on, either, but I went and learned instead of calling everyone pathetic and feeble.

>> ^ForgedReality:

>> ^Payback:
Ok, I thought this was going to be an illusion... Kept waiting for the bigger piece to end up the same size as the smaller one.

Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.

@ForgedReality: You weren't downvoted because you're smart and we're dumb. You're just a dick. Though I will agree that it's somewhat surprising that very few people know of this illusion. Isn't this taught in high school geometry classes? If you're lucky enough to get into a GATE program you learn this in elementary school, so maybe I'm wrong and this type of thing is saved for the elite.

http://en.wikipedia.org/wiki/Missing_square_puzzle

>> ^ForgedReality:
>> ^Payback:
Ok, I thought this was going to be an illusion... Kept waiting for the bigger piece to end up the same size as the smaller one.

Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.


Well, a bit mysterious. The total area inside the bounding box doesn't change, and the pieces fill it, so the sum of their areas would seem to be the total area of the bounding box. You shouldn't be able to "rearrange" the pieces to create a largish hole, because no matter what you do, the sum of the areas of the pieces remain constant and seemingly equal to the area inside the box. The first arrangement is obviously not perfectly filled, and the second one moves those errors to one square area.

Actually, if you look at the template for the puzzle, the area is initially perfectly filled - the guy just made bad cuts. The trick is that the L-pieces are slightly longer at their base than the narrower quadrilaterall; they have to be wedged back into the puzzle space for the second configuration which creates the extra space. The triangle at the top is a true triangle as the cut is just a straight line, so it's a slightly different illusion than the missing square puzzle.
>> ^Payback:

>> ^ForgedReality:
>> ^Payback:
Ok, I thought this was going to be an illusion... Kept waiting for the bigger piece to end up the same size as the smaller one.

Exactly my point. People downvoted my comment because they're dumb, I guess.
The angle cut allows the differently sized pieces to swap places, and changing the configuration of the two L-shaped ones creates a gap. OOOH SO MYSTERIOUS.

Well, a bit mysterious. The total area inside the bounding box doesn't change, and the pieces fill it, so the sum of their areas would seem to be the total area of the bounding box. You shouldn't be able to "rearrange" the pieces to create a largish hole, because no matter what you do, the sum of the areas of the pieces remain constant and seemingly equal to the area inside the box. The first arrangement is obviously not perfectly filled, and the second one moves those errors to one square area.

Fuckin' puzzles, how do they work?

Do the maths, the hole appears because the second configuration is slightly taller, the left hand edges of the two quads are not equal in length. Watch closely, the pieces have to be squashed inside the same sized square, but fit neatly when reset. Mathematically impossible in a rigid world, but physically possible in the real world.

Hasn't the Sift seen this on QI yet? The big triangle on top is not a triangle.

>> ^xxovercastxx:


>> ^crotchflame:


Just to show you guys this shit is not as impossible as you seem to want to believe, I mocked this puzzle up in Photoshop real quick and animated it. In my model, there are VERY slight gaps between some of the pieces. This is due to the fact that the shapes have to be very precise because of the importance of their proportions in relation to each other. The horizontal and vertical parts of the L-pieces get their widths and heights from the differences in width and height between the two larger pieces. It's pretty logical, but hard to execute, which could account for the person in the video having apparent difficulty making the pieces fit together right.

http://img188.imageshack.us/img188/9252/puzzle1.gif

Who said it was impossible? Or even difficult for that matter. Your sketch just flipped what I already said. You can make the pieces fit together perfectly in the first configuration - in fact, the whole puzzle is supposed to be constructed from a single sheet. It then doesn't fit together perfectly in the second configuration but is close enough to look like it. You seem to have made things fit in the second configuration leaving small gaps in the first. It works just as well but seems more difficult to me.

it's quite a nice animation, by the way.

>> ^ForgedReality:

>> ^xxovercastxx:

>> ^crotchflame:

Just to show you guys this shit is not as impossible as you seem to want to believe, I mocked this puzzle up in Photoshop real quick and animated it. In my model, there are VERY slight gaps between some of the pieces. This is due to the fact that the shapes have to be very precise because of the importance of their proportions in relation to each other. The horizontal and vertical parts of the L-pieces get their widths and heights from the differences in width and height between the two larger pieces. It's pretty logical, but hard to execute, which could account for the person in the video having apparent difficulty making the pieces fit together right.
http://img188.imageshack.us/img188/9252/puzzle1.gif

>> ^ForgedReality:

Just to show you guys this shit is not as impossible as you seem to want to believe, I mocked this puzzle up in Photoshop real quick and animated it. In my model, there are VERY slight gaps between some of the pieces. This is due to the fact that the shapes have to be very precise because of the importance of their proportions in relation to each other. The horizontal and vertical parts of the L-pieces get their widths and heights from the differences in width and height between the two larger pieces. It's pretty logical, but hard to execute, which could account for the person in the video having apparent difficulty making the pieces fit together right.
http://img188.imageshack.us/img188/9252/puzzle1.gif


Nobody said it was impossible, only that it doesn't seem like it should work. If you've got 12 sq ft of carpet in a 12 sq ft room, the carpet should cover the floor no matter how you arrange it, as long as there are no overlaps.

What I'd like to understand better is why it works. I've seen several plausible but contradictory explanations.

>> ^xxovercastxx:

>> ^ForgedReality:
Just to show you guys this shit is not as impossible as you seem to want to believe, I mocked this puzzle up in Photoshop real quick and animated it. In my model, there are VERY slight gaps between some of the pieces. This is due to the fact that the shapes have to be very precise because of the importance of their proportions in relation to each other. The horizontal and vertical parts of the L-pieces get their widths and heights from the differences in width and height between the two larger pieces. It's pretty logical, but hard to execute, which could account for the person in the video having apparent difficulty making the pieces fit together right.
http://img188.imageshack.us/img188/9252/puzzle1.gif

Nobody said it was impossible, only that it doesn't seem like it should work. If you've got 12 sq ft of carpet in a 12 sq ft room, the carpet should cover the floor no matter how you arrange it, as long as there are no overlaps.
What I'd like to understand better is why it works. I've seen several plausible but contradictory explanations.


It only works BECAUSE those L-shaped pieces exist. For example, if they had been just two flat slabs, one on top of the other, obviously, it would not work without squishing them both in one or the other configuration. But because they have the shape that they do, and that their proportions are (in the ideal situation) exact and precise, they are able to shift without leaving gaps between the other pieces, but creating the hole between them while still filling out the same area.

They don't COVER the same area because of their shape, but shifting them in this way is creating the same type of result that you would have in the first example I gave, of two flat slabs squishing or distorting--instead of physically changing their shape, since they have those overhangs, you can just shift their positioning, and it has the same effect. Had they been squares, they would have simply overlapped a little instead of creating a hole.